So just came back from vacation in Cancun and took a couple of pounds of white beach sand with me. My wife wanted only a small vial full for remembrance's sake but it looked so good that I was thinking of putting it in my spare tank. Would this be okay, given that it's probably very salty at the moment? Will rinsing in tap water a couple of times help to make this okay for a planted freshwater habitat? Anything else I should be aware of?

I would not do it.
There's too many minerals in there that do not belong in a freshwater aquarium, bacteria, and the sand will alter your pH dramatically.
You can get playsand rather cheap at hardware stores.

+1 for Vilmarisv response. Beach sand and lake sand do have different compositions and the introduction of saltwater sand to a fresh water tank can make the pH tank if you have soft water.

The other thing you have to take into account is pollution. The the sand you collected could have anything from spilled soda to bird poop in it. Not to mention the everyday pollution in our oceans that get introduced to the sand everytime a wave crashes. There are some microscopic bugs you just can't rinse away with water. The random stuff in sea water may not be deadly to humans while we are spending a day on the beach but it would be harmful in a tank.

You are better off buying sand in a bag that you know works for freshwater set ups and isn't contaminated with anything. I personally prefer (black) aquarium sand over playsand (I think it only comes in white), but either type is easy to get online or in stores. I think other members use pool filter sand without problems if you want a third option.

Unfortunately you can't use the beach sand safely even in a saltwater set up. Think of it as a really heavy keepsake. :)